Filters of residuated lattices and triangle algebras
This paper presents in a very systematic and organized way some definitions and results on filters of residuated lattices, like for example prime filters, prime filters of the second and of the third kind, Boolean filters and Boolean filters of the second kind, and related properties on the quotients. Many useful examples on finite residuated lattices are given. Such definitions are extended to triangle algebras, which are interesting algebraic structures, introduced by the authors in [Fuzzy Sets Syst. 159, No.~9, 1042--1060 (2008; Zbl 1174.03028)], corresponding to interval-valued residuated lattices. Some results are given for these structures.
scientific article; zbMATH DE number 5777796
scientific article